Nonlinear transport of rarefied Couette flows from low speed to high speed

Abstract

The nonlinear transport properties and macroscopic flow features of rarefied plane Couette flows from low speed to high speed for a monatomic gas are investigated in detail using the direct simulation Monte Carlo (DSMC) method. The effective viscosity and thermal conductivity are directly computed from the DSMC results according to the linear constitutive relations. The detailed structure of the Knudsen layer (KL) and the functional dependence of the effective transport coefficients on local Knudsen numbers in the whole system are presented and compared with existing theoretical models. The results show that the effective viscosity and thermal conductivity distributions in the KL for different Mach number flows can be recast into the same profile (i.e., isothermal scaling function) in terms of a scaled wall distance η=∫0y1/λ(y)dy, though the local flow is nonisothermal. For all cases, the shear-stress Knudsen number distributions across the channel show a well opposite trend to the effective transport coefficient profiles. The functional dependence between them in the bulk region always coincides with the normal solution that is derived from the Boltzmann model equations for unbounded shear flows, while that in the KL for low-speed cases shows a large difference with the normal solution. As the Mach number increases, the DSMC data in the KL can also agree approximately with the normal solution at a large shear-stress Knudsen number. These results can be very useful for developing phenomenological models to describe a wall-bounded rarefied shear flow, showing a good prospect in both microflow and high-altitude applications.